How to choose between two uncertainty calculation method?

In summary, the speaker is seeking advice on how to perform an error analysis for their experimental work. They have measured temperatures and mass flow rate in a heat exchanger and want to calculate power and uncertainty. They have two equations for calculating uncertainty and are unsure which one to use. They also mention that their measurements were not repeated in the same conditions. The expert suggests using equation 2 if the accuracies are independent and standard deviations, and equation 1 if the accuracies are systematic errors.
  • #1
Helena17
6
0
Hello,
I have made an experimental work and I am ask to provide a formal experimental error analysis. I have a difficulty to choose the appropriate analysis way and would like to have some advices or explanations.
I have measured a temperatures at the intlet (Ti) and outlet (To) of a heat exchanger and the mass flow rate of the fluid. I can calculate the power:
Q = mC (To-Ti)
From what I learn on uncertainty calculations, I am a little bit confused. I finally found that I could calculate my uncertainty in two ways:
(1): [itex]\frac{ΔQ}{Q}[/itex] = [itex]\frac{Δm}{m}[/itex]+ [itex]\frac{2ΔT}{To-Ti}[/itex]

(2): [itex]\frac{ΔQ}{Q}[/itex] =[itex]\sqrt{\left(\frac{Δm}{m}\right)^2+\left(\frac{2ΔT}{To-Ti}\right)^2}[/itex]

Δm: accuracy of the mass flowrate meter (documentation of the supplier)
ΔT: accuracy of the mass flowrate meter (value given by the calibration center)
C is admit as a constant

I made just one measurement. Which one of the above equations must I use and why?

Actually, I derived heat transfer coefficients (built a curve) from several measurements, by changing the flowrate m and the inlet temperature Ti. But no test has been repeated in the same conditions. Is the first method or the second one am I going to use for the "error analysis"?
Thank you in advance.
P.S. Please, even if you do not have a time, even a short answer would be useful for me.
 
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  • #2
Helena17 said:
Hello,
I have made an experimental work and I am ask to provide a formal experimental error analysis. I have a difficulty to choose the appropriate analysis way and would like to have some advices or explanations.
I have measured a temperatures at the intlet (Ti) and outlet (To) of a heat exchanger and the mass flow rate of the fluid. I can calculate the power:
Q = mC (To-Ti)
From what I learn on uncertainty calculations, I am a little bit confused. I finally found that I could calculate my uncertainty in two ways:
(1): [itex]\frac{ΔQ}{Q}[/itex] = [itex]\frac{Δm}{m}[/itex]+ [itex]\frac{2ΔT}{To-Ti}[/itex]

(2): [itex]\frac{ΔQ}{Q}[/itex] =[itex]\sqrt{\left(\frac{Δm}{m}\right)^2+\left(\frac{2ΔT}{To-Ti}\right)^2}[/itex]

Δm: accuracy of the mass flowrate meter (documentation of the supplier)
ΔT: accuracy of the mass flowrate meter (value given by the calibration center)
C is admit as a constant

I made just one measurement. Which one of the above equations must I use and why?

Actually, I derived heat transfer coefficients (built a curve) from several measurements, by changing the flowrate m and the inlet temperature Ti. But no test has been repeated in the same conditions. Is the first method or the second one am I going to use for the "error analysis"?
Thank you in advance.
P.S. Please, even if you do not have a time, even a short answer would be useful for me.


If the two accuracies are independent and the numbers you have giving us are standard deviations then use equation 2. The reason is that independent errors tend to cancel to some degree, so to "add" them correctly one must use the formula you show there.
 
  • #3
Thank you ImaLooser for your explanation. I assume that the accuracies are independant. But I don't know if the accuracy of the intruments are standard deviation (I always think that they are the maximal error; I may be wrong). Actually, for a long time, I do not realize that the accuracy of an instrument can be given as a standard deviation. So, in case, it is the maximal error, should I keep equation (2)?
Thank you.
 
  • #4
Helena17 said:
Thank you ImaLooser for your explanation. I assume that the accuracies are independant. But I don't know if the accuracy of the intruments are standard deviation (I always think that they are the maximal error; I may be wrong). Actually, for a long time, I do not realize that the accuracy of an instrument can be given as a standard deviation. So, in case, it is the maximal error, should I keep equation (2)?
Thank you.

If it is standard deviation then use 2. If it is systematic error, then use 1.

Systematic error is repeatable error. The system always gives exactly the same answer, but the answer is inaccurate in the same way every time.

If it is some unknown kind of error, then use 1. It will always be greater than 2, so you are playing it safe.
 
  • #5
Thank you very much. I understand now the difference.
 

1. What are the two main methods for calculating uncertainty?

The two main methods for calculating uncertainty are the Type A (statistical) method and the Type B (non-statistical) method. The Type A method involves using statistical tools such as standard deviation and confidence intervals to estimate uncertainty, while the Type B method involves using expert judgment and external data to estimate uncertainty.

2. How do I determine which method is appropriate for my data?

The method you should use depends on the type of data you have and the level of accuracy required. If your data is well-suited for statistical analysis and you need a high level of precision, the Type A method may be more appropriate. If your data is more difficult to analyze or you need a rough estimate of uncertainty, the Type B method may be a better choice.

3. Can I use both methods for the same calculation?

Yes, it is possible to use both the Type A and Type B methods for the same calculation. This can be useful in cases where you want to have a more comprehensive understanding of uncertainty by incorporating both statistical and non-statistical factors.

4. Are there any limitations to these methods?

Both the Type A and Type B methods have their own limitations. The Type A method assumes that your data follows a normal distribution and may not be suitable for all types of data. The Type B method relies heavily on expert judgment and external data, which may introduce bias or error into the uncertainty calculation.

5. How can I improve the accuracy of my uncertainty calculation?

To improve the accuracy of your uncertainty calculation, you can increase the sample size, use more precise equipment, or conduct a more thorough analysis of your data. It is also important to carefully consider the assumptions and limitations of each method and choose the most appropriate one for your specific situation.

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